生成雅可比方程的弱解

IF 1.4 4区工程技术 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Mathematics in Engineering Pub Date : 2022-01-01 DOI:10.3934/mine.2023064

F. Jiang

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引用次数: 1

摘要

在生成函数和域的适当假设下，证明了生成的雅可比方程弱解的两组关系，分别是最优运输情况和标准monge - amp情况的推广。一类弱溶液是Aleksandrov溶液、Brenier溶液和C -粘度溶液。另一类弱溶液是Trudinger溶液和L^p -粘度溶液。

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Weak solutions of generated Jacobian equations

We prove two groups of relationships for weak solutions to generated Jacobian equations under proper assumptions on the generating functions and the domains, which are generalizations for the optimal transportation case and the standard Monge-Ampère case respectively. One group of weak solutions is Aleksandrov solution, Brenier solution and $ C $-viscosity solution. The other group of weak solutions is Trudinger solution and $ L^p $-viscosity solution.

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来源期刊

Mathematics in Engineering MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.20

自引率

0.00%

发文量

审稿时长

12 weeks